Calculate Numbers of Plate

5/24/2018 Calculate Numbers of Plate

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Calculate Numbers of Plate/Pipe/Strip

Earthings(Part-1)March 8, 201324 Comments

Introduction:

Number of Earthing Electrode and Earthing Resistance depends on the resistivity of soiland time for fault Current to pass through (1 sec or 3 sec). If we divide the area for

earthing required by the area of one earth plate gives the no of Earth pits required.

There is no general rule to calculate the exact no of earth Pits and Size of Earthing Strip,But discharging of leakage current is certainly dependent on the cross section area of the

material so for any equipment the earth strip size is calculated on the current to be

carried by that strip.First the leakage current to be carried is calculated and then size of

the strip is determined.

For most of the Electrical equipments like Transformer, DG set etc., the General conceptis to have 4 no earth pits.2 nos for body earthing With 2 separate strips with the pitsshorted and 2 nos for Neutral with 2 separate strips with the pits shorted.

The Size of Neutral Earthing Strip should be Capable to carry neutral current ofthat equipment.

The Size of Body Earthing should be capable to carry half of neutral Current. For example for 100kVA transformer, the full load Current is around 140A.The strip

connected should be Capable to carry at least 70A (neutral current) which means a Strip

of GI 25x3mm should be enough to carry the current And for body a strip of 253 will dothe needful.

Normally we consider the strip size that is generally used as Standards. However a stripwith lesser size which can carry a current of 35A can be used for body earthing. Thereason for using 2 earth pits for each body and neutral and then shorting them is to serve

as back up. If one strip gets Corroded and cuts the continuity is broken and the other

Leakage current flows through the other run thery by completing the circuit. Similarly forpanels the no of pits should be 2 nos. The size can be decided on the main incomer

Breaker.

For example if main incomer to breaker is 400A, then Body earthing for panel can have astrip size of 256 mm Which can easily carry 100A.

Number of earth pits is decided by considering the total Fault current to bedissipated to the ground in case of Fault and the current that can be dissipated by

each earth Pit. Normally the density of current for GI strip can be roughly 200 amps per square cam.

Based on the length and dia of the Pipe used the Number of Earthing Pits can be

finalized.
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(1) Calculate Numbers of Pipe Earthing:

(A) Earthing Resistance & No of Rod for Isolated Earth Pit (Without Buried

Earthing Strip):

The Earth Resistance of Single Rod or Pipe electrode is calculated as per BS 7430: R=/23.14xL (loge (8xL/d)-1) Where =Resistivity of Soil ( Meter), L=Length of Electrode (Meter), D=Diameter of Electrode (Meter) Example: Calculate Isolated Earthing Rod Resistance. The Earthing Rod is 4 Meter Long and

having 12.2mm Diameter, Soil Resistivity 500 Meter. R=500/ (23.144) x (Loge (84/0.0125)-1) =156.19 . The Earth Resistance of Single Rod or Pipe electrode is calculated as per IS 3040:

R=100x/23.14xL (loge(4xL/d)) Where =Resistivity of Soil ( Meter), L=Length of Electrode (cm), D=Diameter of Electrode (cm) Example: Calculate Number of CI Earthing Pipe of 100mm diameter, 3 Meter length. System has

Fault current 50KA for 1 Sec and Soil Resistivity is 72.44 -Meters. Current Density At The Surface of Earth Electrode (As per IS 3043): Max. Allowable Current Density I = 7.571000/(xt) A/m2 Max. Allowable Current Density = 7.571000/(72.44X1)=889.419 A/m2 Surface area of one 100mm dia. 3 meter Pipe= 2 x 3.14 x r x L=2 x 3.14 x 0.05 x3 =

0.942 m2 Max. current dissipated by one Earthing Pipe = Current Density x Surface area of

electrode Max. current dissipated by one Earthing Pipe = 889.419x 0.942 = 837.83 A say 838

Amps Number of Earthing Pipe required =Fault Current / Max.current dissipated by one

Earthing Pipe.

Number of Earthing Pipe required= 50000/838 =59.66 Say 60 Nos. Total Number of Earthing Pipe required = 60 Nos. Resistance of Earthing Pipe (Isolated) R=100x/23.14xLx(loge (4XL/d)) Resistance of Earthing Pipe (Isolated) R=10072.44/23.14x300x(loge

(4X300/10))=7.99 /Pipe Overall resistance of 60 No of Earthing Pipe=7.99/60=0.133 .(B) Earthing Resistance & No of Rod for Isolated Earth Pit (With Buried

Earthing Strip):

Resistance of Earth Strip(R) As per IS 3043 R=/23.14xLx (loge (2xLxL/wt)).


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Example: Calculate GI Strip having width of 12mm , length of 2200 Meter buried in ground at

depth of 200mm,Soil Resistivity is 72.44 -Meter Resistanceof Earth Strip(Re)=72.44/23.14x2200x(loge (2x2200x2200/.2x.012))=0.050

From above Calculation Overall resistance of 60 No of Earthing Pipe (Rp) = 0.133 .And it connected to bury Earthing Strip. Here Net Earthing Resistance=(RpxRe)/(Rp+Re)

Net Earthing Resistance= =(0.1330.05)/(0.133+0.05)=0.036 (C) Total Earthing Resistance & No of Electrode for Group of Electrode

(Parallel):

In cases where a single electrode is not sufficient to provide the desired earth resistance,more than one electrode shall be used. The separation of the electrodes shall be about 4M.

The combined resistance of parallel electrodes is a complex function of several factors,such as the number and configuration of electrode the array.

The Total Resistance of Group of Electrode in different configurations as per BS7430:

Ra=R (1+a/n) Where a= /2X3.14XRXS Where S= Distance between adjustment Rod (Meter), =Factor Given in Table, n= Number of Electrode, =Resistivity of Soil ( Meter), R=Resistance of Single Rod in Isolation ()

Factors for parallel electrodes in line (BS 7430)Number of electrodes (n) Factor ()2 1.0

3 1.66

4 2.15

5 2.54

6 2.87

7 3.15

8 3.39

9 3.61

10 3.8

For electrodes equally spaced around a hollow square, e.g. around the perimeter of abuilding, the equations given above are used with a value of taken from followingTable.

For three rods placed in an equilateral triangle, or in an L formation, a value of = 1.66may be assumed.


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Factors for electrodes in a hollow square(BS 7430)

Number of electrodes (n) Factor ()2 2.71

3 4.51

4 5.48

5 6.13

6 6.63

7 7.03

8 7.36

9 7.65

10 7.9

12 8.3

14 8.6

16 8.9

18 9.2

20 9.4

For Hollow Square Total Number of Electrode (N) = (4n-1). The rule of thumb is that rods in parallel should be spaced at least twice their length to

utilize the full benefit of the additional rods.

If the separation of the electrodes is much larger than their lengths and only a fewelectrodes are in parallel, then the resultant earth resistance can be calculated using the

ordinary equation for resistances in parallel.

In practice, the effective earth resistance will usually be higher than Calculation.Typically, a 4 spike array may provide an improvement 2.5 to 3 times. An 8 spike arraywill typically give an improvement of maybe 5 to 6 times.

The Resistance of Original Earthing Rod will be lowered by Total of 40% for SecondRod, 60% for third Rod,66% for forth Rod

Example: Calculate Total Earthing Rod Resistance of 200 Number arranges in Parallel having 4

Meter Space of each and if it connects in Hollow Square arrangement. The Earthing Rodis 4 Meter Long and having 12.2mm Diameter, Soil Resistivity 500 .

First Calculate Single Earthing Rod Resistance R=500/ (23.144) x (Loge (84/0.0125)-1) =136.23 . Now Calculate Total Resistance of Earthing Rod of 200 Number in Parallel condition. a=500/(23.14x136x4)=0.146 Ra (Parallel in Line) =136.23x (1+100.146/200) =1.67 . If Earthing Rod is connected in Hollow Square than Rod in Each side of Square is

200=(4n-1) so n=49 No.

Ra (In Hollow Square) =136.23x (1+9.40.146/200) =1.61 ..


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Calculate Numbers of Plate/Pipe/StripEarthings(Part-2)

March 20, 20136 Comments

(2)Calculate Number of Plate Earthing:

The Earth Resistance of Single Plate electrode is calculated as per IS 3040: R=/A(3.14/A) Where =Resistivity of Soil ( Meter), A=Area of both side of Plate (m2), Example: Calculate Number of CI Earthing Plate of 600600 mm, System has Fault

current 65KA for 1 Sec and Soil Resistivity is 100 -Meters. Current Density At The Surface of Earth Electrode (As per IS 3043): Max. Allowable Current Density I = 7.571000/(xt) A/m2 Max. Allowable Current Density = 7.571000/(100X1)=757 A/m2 Surface area of both side of single 600600 mm Plate= 2 x lxw=2 x 0.060.06 = 0.72 m2 Max. current dissipated by one Earthing Plate = Current Density x Surface area of

electrode Max. current dissipated by one Earthing Plate =7570.72= 545.04Amps Resistance of Earthing Plate (Isolated)(R)=/A(3.14/A) Resistance of Earthing Plate (Isolated)(R)=100/0.72x(3.14/.072)=290.14 Number of Earthing Plate required =Fault Current / Max.current dissipated by one

Earthing Pipe.

Number of Earthing Plate required= 65000/545.04 =119 Nos. Total Number of Earthing Plate required = 119 Nos. Overall resistance of 119 No of Earthing Plate=290.14/119=2.438 .

(3)Calculating Resistance of Bared Earthing Strip:

1)Calculation for earth resistance of buried Strip (As per IEEE):

The Earth Resistance of Single Strip of Rod buried in ground is R=/Px3.14xL (loge (2xLxL/Wxh)+Q) Where =Resistivity of Soil ( Meter), h=Depth of Electrode (Meter), w=Width of Strip or Diameter of Conductor (Meter) L=Length of Strip or Conductor (Meter) P and Q are Coefficients

2)Calculation for earth resistance of buried Strip(As per IS 3043):

The Earth Resistance of Single Strip of Rod buried in ground is
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R=100x/23.14xL (loge (2xLxL/Wxt)) Where =Resistivity of Soil ( Meter), L=Length of Strip or Conductor (cm) w=Width of Strip or Diameter of Conductor (cm) t= Depth of burial (cm) Example : Calculate Earthing Resistance of Earthing strip/wire of 36mm Diameter, 262 meter long

buried at 500mm depth in ground, soil Resistivity is 65 Meter. Here R = Resistance of earth rod in W. r = Resistivity of soil( Meter) = 65 Meter l = length of the rod (cm) = 262m = 26200 cm d = internal diameter of rod(cm) = 36mm = 3.6cm h = Depth of the buried strip/rod (cm)= 500mm = 50cm Resistance of Earthing Strip/Conductor (R)=/23.14xL (loge (2xLxL/Wt)) Resistance of Earthing Strip/Conductor

(R)=65/23.14x26200xln(2x26200x26200/3.650)

Resistance of Earthing Strip/Conductor (R)== 1.7 ..

Calculate Numbers of Plate/Pipe/StripEarthings(Part-3)April 1, 201314 Comments

Calculate Min. Cross Section area of Earthing Conductor:

Cross Section Area of Earthing Conductor As per IS 3043 Cross Section Area of Earthing Conductor (A) =(If xt) / K Where t= Fault current Time (Second). K= Material Constant. Example: Calculate Cross Section Area of GI Earthing Conductor for System has 50KA Fault

Current for 1 second. Corrosion will be 1.0 % Per Year and No of Year for Replacement

is 20 Years.

Cross Section Area of Earthing Conductor (A) =(If xt) / K Here If=50000 Amp T= 1Second K=80 (Material Constant, For GI=80, copper K=205, Aluminium K=126). Cross Section Area of Earthing Conductor (A) =(500001)/80 Cross Section Area of GI Earthing Conductor (A)=625 Sq.mm Allowance for Corrosion = 1.0 % Per Year & Number of Year before replacement say =

20 Years

Total allowance = 20 x 1.0% = 20%
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Safety factor = 1.5 Required Earthing Conductor size = Cross sectional area x Total allowance x Safety

factor

Required Earthing Conductor size = 1125 Sq.mm say 1200 Sq.mm Hence, Considered 1Nox12x100 mm GI Strip or 2Nox6 x 100 mm GI Strips

Thumb Rule for Calculate Number of Earthing Rod:

The approximate earth resistance of the Rod/Pipe electrodes can be calculated by Earth Resistance of the Rod/Pipe electrodes R= K x /L Where = Resistivity of earth in Ohm-Meter L= Length of the electrode in Meter. d= Diameter of the electrode in Meter. K=0.75 if 25< L/d < 100. K=1 if 100 < L/d < 600 K=1.2 o/L if 600 < L/d < 300 Number of Electrode if find out by Equation of R(d) =(1.5/N) x R Where R(d) = Desired earth resistance R= Resistance of single electrode N= No. of electrodes installed in parallel at a distance of 3 to 4 Meter interval. Example: Calculate Earthing Pipe Resistance and Number of Electrode for getting Earthing

Resistance of 1 ,Soil Resistivity of =40, Length=2.5 Meter, Diameter of Pipe= 38mm.

Here L/d = 2.5/0.038=65.78 so K=0.75 The Earth Resistance of the Pipe electrodes R= K x /L=0.7565.78=12 One electrode the earth resistance is 12 . To get Earth resistance of 1 the total Number of electrodes required =(1.512)/1 =18

No

Calculating Resistance & Number of Earthing Rod:

Reference: As per EHV Transmission Line Reference Book page: 290 and ElectricalTransmission & Distribution Reference Book Westinghouse Electric Corporation,

Section-I Page: 570-590.

Earthing Resistance of Single Rods: R = x[ln (2L/a)-1]/(23.14xL) Earthing Resistance of Parallel Rods: R = x[ln (2L/A]/ (23.14xL) Where L= length of rod in ground Meter, a= radius of rod Meter = ground resistivity, ohm- Meter A= (axS) S= Rod separation Meter


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Factor affects on Ground resistance:

The NEC code requires a minimum ground electrode length of 2.5 meters (8.0 feet) to bein contact with the soil. But, there are some factor that affect the ground resistance of a

ground system:

Length / Depth of the ground electrode: double the length, reduce ground resistance byup to 40%.

Diameter of the ground electrode: double the diameter, lower ground resistance by only10%.

Number of ground electrodes: for increased effectiveness, space additional electrodes atleast equal to the depth of the ground electrodes.

Ground system design: single ground rod to ground plate.

The GI Earthing Conductor sizes for various

Equipments:

No Equipments Earth Strip Size

1 HT switchgear, structures, cable trays &fence, rails, gate and steel column 55 X 6 mm (GI)

2 Lighting Arrestor 25 X 3 mm (Copper)

3 PLC Panel 25 X 3 mm (Copper)

4 DG & Transformer Neutral 50X6 mm (Copper)

5 Transformer Body 50X6 mm (GI)

6 Control & Relay Panel 25 X 6 mm (GI)

7 Lighting Panel & Local Panel 25 X 6 mm (GI)

8 Distribution Board 25 X 6 mm (GI)

9 Motor up to 5.5 kw 4 mm2 (GI)

10 Motor 5.5 kw to 55 kw 25 X 6 mm (GI)11 Motor 22 kw to 55 kw 40 X 6 mm (GI)

12 Motor Above 55 kw 55 X 6 mm (GI)

Selection of Earthing System:

Installations/ Isc

CapacityIR Value

RequiredSoil Type/ Resistivity Earth System
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House holdearthing/3kA

8 ohm Normal Soil/ up to 50 ohm-meter Single Electrode

Sandy Soil/ between 50 to 2000 ohm-

meter

Single Electrode

Rocky Soil/ More than 2000 ohm- meter Multiple Electrodes

Commercial

premises,Office /5kA

2 ohm Normal Soil/ up to 50 ohm-meter Single Electrode

Sandy Soil/ between 50 to 2000 ohm-meter

Multiple Electrodes


Transformers,

substationearthing,LT line equipment/

15kA

less than 1

ohm

Normal Soil/ up to 50 ohm-meter Single Electrode


meter

Multiple Electrodes


LA, High current

Equipment./ 50kA

less than 1

ohm


Sandy Soil/ between 50 to 2000 ohm-meter

Multiple Electrodes

Rocky Soil/ More than 2000 ohm- meter Multiple ElectrodesPRS, UTS, RTUs,

Data processingcentre etc./5KA

less than

0.5 ohm



meter

Multiple Electrodes


Size of Earthing Conductor:

Ref IS 3043 &Handbook on BS 7671: The Lee Wiring Regulations by Trevor E. Marks.

Size of Earthing ConductorArea of Phase Conductor S(mm2)

Area of Earthing conductor(mm2) When It is Same

Material as Phase Conductor

Area of Earthing conductor(mm2) When It is Not Same

Material as Phase Conductor

S < 16 mm2 S SX(k1/k2)

16 mm2 35 mm2 S/2 SX(k1/2k2)

K1 is value of Phase conductor,k2 is value of earthing conductor

Value of K for GI=80, Alu=126,Cu=205 for 1 Sec

Standard Earthing Strip/Plate/Pipe/wire Weight:

GI Earthing Strip:

Size (mm2) Weight

20 x 3 500 gm Per meter

25 x 3 600 gm Per meter


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25 x 6 1/200 Kg Per meter


40 x 6 2 Kg Per meter




GI Earthing Plate:

Plate Weight

600 x 600 x 3 mm 10 Kg App.

600 x 600 x 4 mm 12 Kg App.

600 x 600 x 5 mm 15 Kg App.

600 x 600 x 6 mm 18 Kg App.

600 x 600 x 12 mm 36 Kg App.

1200 x 1200 x 6 mm 70 Kg App.

1200 x 1200 x 12 mm 140 Kg App.

GI Earthing Pipe:

Pipe Weight

3 meter Long BISE 5 Kg App.

3 meter r Long BISE 9 Kg App.

4.5 meter (15 Long BISE) 5 Kg App.4.5 meter (15 Long BISE) 9 Kg App.

4.5 meter (15 Long BISE) 14 Kg App

GI Earthing Wire:

Plate Weight

6 Swg 5 meter in 1 Kg

8 Swg 9 meter in 1 Kg

.

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Contents

[hide]

1 Introductiono 1.1 Why do the calculation?o 1.2 When to do the calculation?o 1.3 When is the calculation unnecessary?

2 Calculation Methodologyo 2.1 Prerequisiteso 2.2 Earthing Grid Conductor Sizingo 2.3 Touch and Step Potential Calculations

2.3.1 Step 1: Soil Resistivity 2.3.2 Step 2: Surface Layer Materials 2.3.3 Step 3: Earthing Grid Resistance

2.3.3.1 Simplified Method 2.3.3.2 Schwarz Equations

2.3.4 Step 4: Maximum Grid Current 2.3.4.1 Current Division Factor 2.3.4.2 Decrement Factor

2.3.5 Step 5: Touch and Step Potential Criteria 2.3.6 Step 6: Ground Potential Rise (GPR) 2.3.7 Step 7: Earthing Grid Design Verification

2.3.7.1 Mesh Voltage Calculation 2.3.7.1.1 Geometric Spacing Factor Km 2.3.7.1.2 Geometric Factor n 2.3.7.1.3 Irregularity Factor Ki 2.3.7.1.4 Effective Buried Length LM

2.3.7.2 Step Voltage Calculation 2.3.7.2.1 Geometric Spacing Factor Ks 2.3.7.2.2 Effective Buried Length LS

2.3.7.3 What Now? 3 Worked Example

o 3.1 Step 1: Soil Resistivityo 3.2 Step 2: Surface Layer Materialso 3.3 Step 3: Earthing Grid Resistanceo 3.4 Step 4: Maximum Grid Currento 3.5 Step 5: Touch and Step Potential Criteriao 3.6 Step 6: Ground Potential Rise (GPR)o 3.7 Step 7: Earthing Grid Design Verification

3.7.1 Mesh Voltage Calculation 3.7.2 Step Voltage Calculation

4 Computer Based Tools 5 What next?
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Introduction

The earthing system in a plant / facility is very important for a few reasons, all of which are

related to either the protection of people and equipment and/or the optimal operation of theelectrical system. These include:

Equipotential bonding of conductive objects (e.g. metallic equipment, buildings, pipingetc) to the earthing system prevent the presence of dangerous voltages between

objects (and earth).

The earthing system provides a low resistance return path for earth faults within theplant, which protects both personnel and equipment

For earth faults with return paths to offsite generation sources, a low resistanceearthing grid relative to remote earth prevents dangerous ground potential rises (touch

and step potentials)

The earthing system provides a low resistance path (relative to remote earth) forvoltage transients such as lightning and surges / overvoltages

Equipotential bonding helps prevent electrostatic buildup and discharge, which cancause sparks with enough energy to ignite flammable atmospheres

The earthing system provides a reference potential for electronic circuits and helpsreduce electrical noise for electronic, instrumentation and communication systems

This calculation is based primarily on the guidelines provided byIEEE Std 80 (2000),"Guide for

safety in AC substation grounding". Lightning protection is excluded from the scope of thiscalculation (refer to the specificlightning protection calculationfor more details).

Why do the calculation?

The earthing calculation aids in the proper design of the earthing system. Using the results of thiscalculation, you can:

Determine the minimum size of the earthing conductors required for the main earthgrid

Ensure that the earthing design is appropriate to prevent dangerous step and touchpotentials (if this is necessary)

When to do the calculation?

This calculation should be performed when the earthing system is being designed. It could also

be done after the preliminary design has been completed to confirm that the earthing system isadequate, or highlight the need for improvement / redesign. Ideally, soil resistivity test results

from the site will be available for use in touch and step potential calculations (if necessary).

When is the calculation unnecessary?
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The sizing of earthing conductors should always be performed, but touch and step potential

calculations (per IEEE Std 80 for earth faults with a return path through remote earth) are not

always necessary.

For example, when all electricity is generated on-site and the HV/MV/LV earthing systems are

interconnected, then there is no need to do a touch and step potential calculation. In such a case,all earth faults would return to the source via the earthing system (notwithstanding some small

leakage through earth).

However, where there are decoupled networks (e.g. long transmission lines to remote areas of

the plant), then touch and step potential calculations should be performed for the remote area

only.

Calculation Methodology

This calculation is based on IEEE Std 80 (2000), "Guide for safety in AC substation grounding".

There are two main parts to this calculation:

Earthing grid conductor sizing Touch and step potential calculations

IEEE Std 80 is quite descriptive, detailed and easy to follow, so only an overview will be

presented here and IEEE Std 80 should be consulted for further details (although references will

be given herein).

Prerequisites

The following information is required / desirable before starting the calculation:

A layout of the site Maximum earth fault current into the earthing grid Maximum fault clearing time Ambient (or soil) temperature at the site Soil resistivity measurements at the site (for touch and step only) Resistivity of any surface layers intended to be laid (for touch and step only)

Earthing Grid Conductor Sizing

Determining the minimum size of the earthing grid conductors is necessary to ensure that theearthing grid will be able to withstand the maximum earth fault current. Like a normal power

cable under fault, the earthing grid conductors experience an adiabatic short circuit temperaturerise. However unlike a fault on a normal cable, where the limiting temperature is that which

would cause permanent damage to the cable's insulation, the temperature limit for earthing grid

conductors is the melting point of the conductor. In other words, during the worst case earthfault, we don't want the earthing grid conductors to start melting!
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The minimum conductor size capable of withstanding the adiabatic temperature rise associated

with an earth fault is given by re-arranging IEEE Std 80 Equation 37:

Where is the minimum cross-sectional area of the earthing grid conductor (mm2)

is the energy of the maximum earth fault (A2s)

is the maximum allowable (fusing) temperature (C)

is the ambient temperature (C)

is the thermal coefficient of resistivity (C- 1)

is the resistivity of the earthing conductor (.cm)

is

is the thermal capacity of the conductor per unit volume(Jcm- 3

C- 1

)

The material constants Tm, r, r and TCAP for common conductor materials can be found inIEEE Std 80 Table 1. For example. commercial hard-drawn copper has material constants:

Tm= 1084 C r= 0.00381 C- 1 r= 1.78 .cm TCAP= 3.42 Jcm- 3C- 1.

As described in IEEE Std 80 Section 11.3.1.1, there are alternative methods to formulate this

equation, all of which can also be derived fromfirst principles).

There are also additional factors that should be considered (e.g. taking into account future growth

in fault levels), as discussed in IEEE Std 80 Section 11.3.3.

Touch and Step Potential Calculations

When electricity is generated remotely and there are no return paths for earth faults other than

the earth itself, then there is a risk that earth faults can cause dangerous voltage gradients in the

earth around the site of the fault (called ground potential rises). This means that someonestanding near the fault can receive a dangerous electrical shock due to:
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Touch voltages - there is a dangerous potential difference between the earth and a metallicobject that a person is touching

Step voltages - there is a dangerous voltage gradient between the feet of a person standing onearth

The earthing grid can be used to dissipate fault currents to remote earth and reduce the voltagegradients in the earth. The touch and step potential calculations are performed in order to assess

whether the earthing grid can dissipate the fault currents so that dangerous touch and stepvoltages cannot exist.

Step 1: Soil Resistivity

The resistivity properties of the soil where the earthing grid will be laid is an important factor in

determining the earthing grid's resistance with respect to remote earth. Soils with lowerresistivity lead to lower overall grid resistances and potentially smaller earthing grid

configurations can be designed (i.e. that comply with safe step and touch potentials).

It is good practice to perform soil resistivity tests on the site. There are a few standard methods

for measuring soil resistivity (e.g. Wenner four-pin method). A good discussion on theinterpretation of soil resistivity test measurements is found in IEEE Std 80 Section 13.4.

Sometimes it isn't possible to conduct soil resistivity tests and an estimate must suffice. Whenestimating soil resistivity, it goes without saying that one should err on the side of caution and

select a higher resistivity. IEEE Std 80 Table 8 gives some guidance on range of soil resistivities

based on the general characteristics of the soil (i.e. wet organic soil = 10 .m, moist soil = 100.m, dry soil = 1,000 .m and bedrock = 10,000 .m).

Step 2: Surface Layer Materials

Applying a thin layer (0.08m - 0.15m) of high resistivity material (such as gravel, blue metal,crushed rock, etc) over the surface of the ground is commonly used to help protect againstdangerous touch and step voltages. This is because the surface layer material increases the

contact resistance between the soil (i.e. earth) and the feet of a person standing on it, thereby

lowering the current flowing through the person in the event of a fault.

IEEE Std 80 Table 7 gives typical values for surface layer material resistivity in dry and wet

conditions (e.g. 40mm crushed granite = 4,000 .m (dry) and 1,200 .m (wet)).

The effective resistance of a person's feet (with respect to earth) when standing on a surface layeris not the same as the surface layer resistance because the layer is not thick enough to haveuniform resistivity in all directions. A surface layer derating factor needs to be applied in order to

compute the effective foot resistance (with respect to earth) in the presence of a finite thicknessof surface layer material. This derating factor can be approximated by an empirical formula as

per IEEE Std 80 Equation 27:
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Where is the surface layer derating factor

is the soil resistivity (.m)

is the resistivity of the surface layer material (.m)

is the thickness of the surface layer (m)

This derating factor will be used later in Step 5 when calculating the maximum allowable touchand step voltages.

Step 3: Earthing Grid Resistance

A good earthing grid has low resistance (with respect to remote earth) to minimise groundpotential rise (GPR) and consequently avoid dangerous touch and step voltages. Calculating the

earthing grid resistance usually goes hand in hand with earthing grid design - that is, you design

the earthing grid to minimise grid resistance. The earthing grid resistance mainly depends on the

area taken up by the earthing grid, the total length of buried earthing conductors and the numberof earthing rods / electrodes.

IEEE Std 80 offers two alternative options for calculating the earthing grid resistance (withrespect to remote earth) - 1) the simplified method (Section 14.2) and 2) the Schwarz equations

(Section 14.3), both of which are outlined briefly below. IEEE Std 80 also includes methods forreducing soil resistivity (in Section 14.5) and a treatment for concrete-encased earthingelectrodes (in Section 14.6).

Simplified Method

IEEE Std 80 Equation 52 gives the simplified method as modified by Sverak to include the effectof earthing grid depth:

Where is the earthing grid resistance with respect to remote earth ()

is the soil resistivitiy (.m)

is the total length of buried conductors (m)


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is the total area occupied by the earthing grid (m2)

is the depth of the earthing grid (m)

Schwarz Equations

The Schwarz equations are a series of equations that are more accurate in modelling the effect of

earthing rods / electrodes. The equations are found in IEEE Std 80 Equations 53, 54, 55(footnote)

and 56, as follows:

Where is the earthing grid resistance with respect to remote earth ()

is the earth resistance of the grid conductors ()

is the earth resistance of the earthing electrodes ()

is the mutual earth resistance between the grid conductors and earthing electrodes ()

And the grid, earthing electrode and mutual earth resistances are:

Where is the soil resistivity (.m)

is the total length of buried grid conductors (m)

is for conductors buried at depth metres and with cross-sectional radius

metres, or simply for grid conductors on the surface

is the total area covered by the grid conductors (m2)
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is the length of each earthing electrode (m)

is number of earthing electrodes in area

is the cross-sectional radius of an earthing electrode (m)

and are constant coefficients depending on the geometry of the grid

The coefficient can be approximated by the following:

(1) For depth :

(2) For depth :

(3) For depth :The coefficient can be approximated by the following:

(1) For depth :

(2) For depth :

(3) For depth :

Where in both cases, is the length-to-width ratio of the earthing grid.

Step 4: Maximum Grid Current

The maximum grid current is the worst case earth fault current that would flow via the earthinggrid back to remote earth. To calculate the maximum grid current, you firstly need to calculate

the worst case symmetrical earth fault current at the facility that would have a return path

through remote earth (call this ). This can be found from the power systems studies or from

manual calculation. Generally speaking, the highest relevant earth fault level will be on the

primary side of the largest distribution transformer (i.e. either the terminals or the deltawindings).

Current Division Factor

Not all of the earth fault current will flow back through remote earth. A portion of the earth faultcurrent may have local return paths (e.g. local generation) or there could be alternative return


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paths other than remote earth (e.g. overhead earth return cables, buried pipes and cables, etc).

Therefore a current division factor must be applied to account for the proportion of the fault

current flowing back through remote earth.

Computing the current division factor is a task that is specific to each project and the fault

location and it may incorporate some subjectivity (i.e. "engineeing judgement"). In any case,IEEE Std 80 Section 15.9 has a good discussion on calculating the current division factor. In the

most conservative case, a current division factor of can be applied, meaning that 100%

of earth fault current flows back through remote earth.

The symmetrical grid current is calculated by:

Decrement Factor

The symmetrical grid current is not the maximum grid current because of asymmetry in shortcircuits, namely a dc current offset. This is captured by the decrement factor, which can becalculated from IEEE Std 80 Equation 79:

Where is the decrement factor

is the duration of the fault (s)

is the dc time offset constant (see below)

The dc time offset constant is derived from IEEE Std 80 Equation 74:

Where is the X/R ratio at the fault location

is the system frequency (Hz)

The maximum grid current is lastly calculated by:


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Step 5: Touch and Step Potential Criteria

One of the goals of a safe earthing grid is to protect people against lethal electric shocks in the

event of an earth fault. The magnitude of ac electric current (at 50Hz or 60Hz) that a humanbody can withstand is typically in the range of 60 to 100mA, when ventricular fibrillation and

heart stoppage can occur. The duration of an electric shock also contributes to the risk ofmortality, so the speed at which faults are cleared is also vital. Given this, we need to prescribe

maximum tolerable limits for touch and step voltages that do not lead to lethal shocks.

The maximum tolerable voltages for step and touch scenarios can be calculated empirically from

IEEE Std Section 8.3 for body weights of 50kg and 70kg:

Touch voltage limit - the maximum potential difference between the surface potential and the

potential of an earthed conducting structure during a fault (due to ground potential rise):

50kg person:

70kg person:Step voltage limit - is the maximum difference in surface potential experience by a person

bridging a distance of 1m with the feet without contact to any earthed object:

50kg person:

70kg person:Where is the touch voltage limit (V)

is the step voltage limit (V)

is the surface layer derating factor (as calculated inStep 2)

is the soil resistivity (.m)

is the maximum fault clearing time (s)
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The choice of body weight (50kg or 70kg) depends on the expected weight of the personnel atthe site. Typically, where women are expected to be on site, the conservative option is to choose

50kg.

Step 6: Ground Potential Rise (GPR)

Normally, the potential difference between the local earth around the site and remote earth is

considered to be zero (i.e. they are at the same potential). However an earth fault (where the fault

current flows back through remote earth), the flow of current through the earth causes localpotential gradients in and around the site. The maximum potential difference between the site

and remote earth is known as the ground potential rise (GPR). It is important to note that this is a

maximum potential potential difference and that earth potentials around the site will varyrelative to the point of fault.

The maximum GPR is calculated by:

Where is the maximum ground potential rise (V)

is the maximum grid current found earlier inStep 4(A)

is the earthing grid resistance found earlier inStep 3()

Step 7: Earthing Grid Design Verification

Now we just need to verify that the earthing grid design is safe for touch and step potential. If themaximum GPR calculated above does not exceed either of the touch and step voltage limits

(fromStep 5), then the grid design is safe.

However if it does exceed the touch and step voltage limits, then some further analysis is

required to verify the design, namely the calculation of the maximum mesh and step voltages as

per IEEE Std 80 Section 16.5.

Mesh Voltage Calculation

The mesh voltage is the maximum touch voltage within a mesh of an earthing grid and is derived

from IEEE Std 80 Equation 80:

Where :: is the soil resistivity (.m)
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is the geometric spacing factor (see below)

is the irregularity factor (see below)

is the effective buried length of the grid (see below)

Geometric Spacing Factor Km

The geometric spacing factor is calculated from IEEE Std 80 Equation 81:

Where is the spacing between parallel grid conductors (m)

is the depth of buried grid conductors (m)

is the cross-sectional diameter of a grid conductor (m)

is a weighting factor for depth of burial =

is a weighting factor for earth electrodes /rods on the corner mesh

for grids with earth electrodes along the grid perimeter or corners

for grids with no earth electrodes on the corners or on the perimeteris a geometric factor (see below)

Geometric Factor n

The geometric factor is calculated from IEEE Std 80 Equation 85:

With
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for square grids, or otherwise

for square and rectangular grids, or otherwise

for square, rectangular and L-shaped grids, or otherwise

Where is the total length of horizontal grid conductors (m)

is the length of grid conductors on the perimeter (m)

is the total area of the grid (m2)

and are the maximum length of the grids in the x and y directions (m)

is the maximum distance between any two points on the grid (m)

Irregularity Factor Ki

The irregularity factor is calculated from IEEE Std 80 Equation 89:

Where is the geometric factor derived above

Effective Buried Length LM

The effective buried length is found as follows:

For grids with few or no earthing electrodes (and none on corners or along the perimeter):


is the total length of earthing electrodes / rods (m)

For grids with earthing electrodes on the corners and along the perimeter:


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is the length of each earthing electrode / rod (m)

and are the maximum length of the grids in the x and y directions (m)

Step Voltage Calculation

The maximum allowable step voltage is calculated from IEEE Std 80 Equation 92:

Where :: is the soil resistivity (.m)


is the geometric spacing factor (see below)

is the irregularity factor (asderived abovein the mesh voltage calculation)

is the effective buried length of the grid (see below)

Geometric Spacing Factor Ks

The geometric spacing factor based on IEEE Std 80 Equation 81 is applicable for burialdepths between 0.25m and 2.5m:

Where is the spacing between parallel grid conductors (m)

is the depth of buried grid conductors (m)

is a geometric factor (asderived abovein the mesh voltage calculation)
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Effective Buried Length LS

The effective buried length for all cases can be calculated by IEEE Std 80 Equation 93:



What Now?

Now that the mesh and step voltages are calculated, compare them to the maximum tolerable

touch and step voltages respectively. If:

, and

then the earthing grid design is safe.

If not, however, then further work needs to be done. Some of the things that can be done to make

the earthing grid design safe:

Redesign the earthing grid to lower the grid resistance (e.g. more grid conductors, moreearthing electrodes, increasing cross-sectional area of conductors, etc). Once this is

done, re-compute the earthing grid resistance (seeStep 3)and re-do the touch and step

potential calculations.

Limit the total earth fault current or create alternative earth fault return paths Consider soil treatments to lower the resistivity of the soil Greater use of high resistivity surface layer materials

Worked Example

In this example, the touch and step potential calculations for an earthing grid design will be

performed. The proposed site is a small industrial facility with a network connection via a

transmission line and a delta-wye connected transformer.

Step 1: Soil Resistivity

The soil resistivity around the site was measured with a Wenner four-pin probe and found to beapproximately 300 .m.
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Step 2: Surface Layer Materials

A thin 100mm layer of blue metal (3,000 .m) is proposed to be installed on the site. Thesurface layer derating factor is:

Step 3: Earthing Grid Resistance

Figure 1. Proposed rectangular earthing grid

A rectangular earthing grid (see the figure right) with the following parameters is proposed:

Length of 90m and a width of 50m 6 parallel rows and 7 parallel columns Grid conductors will be 120 mm2and buried at a depth of 600mm 22 earthing rods will be installed on the corners and perimeter of the grid Each earthing rod will be 3m long

Using the simplified equation, the resistance of the earthing grid with respect to remote earth is:
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Step 4: Maximum Grid Current

Suppose that the maximum single phase to earth fault at the HV winding of the transformer is

3.1kA and that the current division factor is 1 (all the fault current flows back to remote earth).

The X/R ratio at the fault is approximately 15, the maximum fault duration 150ms and the

system nominal frequency is 50Hz. The DC time offset is therefore:

The decrement factor is then:

Fianlly, the maximum grid current is:

kA

Step 5: Touch and Step Potential Criteria


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Based on the average weight of the workers on the site, a body weight of 70kg is assumed for the

maximum touch and step potential. A maximum fault clearing time of 150ms is also assumed.

The maximum allowable touch potential is:

V

The maximum allowable step potential is:

V

Step 6: Ground Potential Rise (GPR)

The maximum ground potential rise is:

V

The GPR far exceeds the maximum allowable touch and step potentials, and further analysis ofmesh and step voltages need to be performed.

Step 7: Earthing Grid Design Verification

Mesh Voltage Calculation

The components of the geometric factor , , and for the rectangular grid are:


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Therefore the geometric factor is:

The average spacing between parallel grid conductors is:

where and are the width and length of the grid respectively (e.g. 50m and 90m)

and is the number of parallel rows and columns respectively (e.g. 6 and 7)

The geometric spacing factor is:


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The irregularity factor is:

The effective buried length is:

m

Finally, the maximum mesh voltage is:

V

The maximum allowable touch potential is 1,720V, which exceeds the mesh voltage calculatedabove and the earthing system passes the touch potential criteria (although it is quite marginal).

Step Voltage Calculation

The geometric spacing factor is:


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The effective buried length is:

m

Finally, the maximum allowable step voltage is:

V

The maximum allowable step potential is 5,664V, which exceeds the step voltage calculatedabove and the earthing system passes the step potential criteria. Having passed both touch and

step potential criteria, we can conclude that the earthing system is safe.

Computer Based Tools


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Figure 2. PTW GroundMat software output (courtesy of SKM Systems Analysis Inc)

As can be seen from above, touch and step potential calculations can be quite a tedious andlaborious task, and one that could conceivably be done much quicker by a computer. Even IEEE

Std 80 recommends the use of computer software to calculate grid resistances, and mesh and stepvoltages, and also to create potential gradient visualisations of the site.

Computer software packages can be used to assist in earthing grid design by modeling andsimulation of different earthing grid configurations. The tools either come as standalone

packages or plug-in modules to power system analysis software (such as PTW'sGroundMator

ETAP's Ground Grid Design Assessment. Examples of standalone packages include SESAutogridandSafeGrid.

What next?

The minimum size for the earthing grid conductors can be used to specify the earthing grid

conductor sizes in the material take-offs and earthing drawings. The touch and step potential

calculations (where necessary) verify that the earthing grid design is safe for the worst earth

faults to remote earth. The earthing drawings can therefore be approved for the next stage ofreviews.

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